Principal specialization of dual characters of flagged Weyl modules

TL;DR

This paper investigates the principal specialization of dual characters of flagged Weyl modules, providing an alternative proof of Stanley's conjecture on Schubert polynomials' principal specialization.

Contribution

It offers a new approach to understanding the principal specialization of dual characters of flagged Weyl modules, connecting it to Schubert polynomials and providing an alternative proof of a conjecture.

Findings

Established a new proof of Stanley's conjecture on Schubert polynomials.

Connected dual characters of flagged Weyl modules to Schur and Schubert polynomials.

Enhanced understanding of principal specialization in algebraic combinatorics.

Abstract

Schur polynomials are special cases of Schubert polynomials, which in turn are special cases of dual characters of flagged Weyl modules. The principal specialization of Schur and Schubert polynomials has a long history, with Macdonald famously expressing the principal specialization of any Schubert polynomial in terms of reduced words. We study the principal specialization of dual characters of flagged Weyl~modules. Our result yields an alternative proof of a conjecture of Stanley about the principal specialization of Schubert polynomials, originally proved by Weigandt.